Trajectory pattern extraction to climate data and climate change analytics

<p style="margin-top:8px; margin-bottom:8px; text-align:justify; text-indent:21.0pt"><span style="font-size:10.5pt"><span style="text-justify:inter-ideograph"><span style="layout-grid-mode:both"><span style="font-family:Arial,sans-serif"><span style="color:black"><span lang="EN-US" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"><span style="layout-grid-mode:both">Climate data contains rich information and show high dimensions. Through exploring the data trajectory of climate data, climate change can be forecasted. Climate data is typical high-dimensional data, unlike shallow structures, deep structures have more advantages in handling high-dimensional data. Deep neural networks with multiple layers have ability of the data trajectory discovery from the complicated high-dimensional data. Here, this paper seeks to explore the data trajectory from complicated climate data using the proposed deep neural networks. First, using the sampling theorem to reconstruct the discrete surface that can converge to the original space. Thereafter, </span></span></span><span lang="EN-US" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif">to minimize the error between the original data trajectory and the extracted data trajectory, </span></span><span lang="EN-US" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"><span style="layout-grid-mode:both">the Brenier theoretical function in Brenier Theorem is used as the loss function of the deep neural networks. By doing so, the deep neural networks </span></span></span><span lang="EN-US" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif">can extract the data trajectory from climate data as accurate as possible</span></span><span lang="EN-US" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"><span style="layout-grid-mode:both">. Finally, as an important application, since a thorough understanding of the data trajectory of climate data is essential for understanding the effect of earth’s future climate.</span></span></span></span></span></span></span></span></p>